Getting Started 
Misconception/Error The student does not understand how to use trigonometric ratios to solve the problem. 
Examples of Student Work at this Level The student may add some of the given information to the diagram. However, the student:
 Draws the diagram incorrectly and is unable to use it to find any length in the diagram.
 Indicates he or she does not know how to write an equation to solve the problem.
 Writes an equation that does not involve a trigonometric ratio such as 210 = .

Questions Eliciting Thinking Where on your diagram is the lighthouse? The first boat? The second boat?
What were you given? What are you trying to find?
Can this situation be modeled by a right triangle? 
Instructional Implications If necessary, review the concepts of angles of elevation and depression. Guide the student to observe that in any given diagram, the angle of elevation and the angle of depression form an alternate interior pair and are, therefore, congruent. Provide opportunities for the student to identify angles of elevation and depression in a variety of diagrams and contexts. Assist the student in drawing a diagram involving a right triangle that models the relationships among the values given in the problem. Make clear the location of the right angle.
Review the definitions of the trigonometric ratios. Provide opportunities to apply the definitions to right triangles (presented in various orientations) by asking the student to identify the sine, cosine, and tangent ratios associated with each of the two acute angles. Then model finding an unknown length or angle measure in a right triangle by using an appropriate trigonometric ratio. Caution the student to carefully select an appropriate ratio and substitute measures correctly to write an equation. If needed, review solving equations of the form with the unknown in all positions.
Provide additional opportunities to find an unknown length or angle measure in right triangles by using the Pythagorean Theorem or an appropriate trigonometric ratio.
Consider implementing other MFAS tasks for GSRT.3.8. 
Moving Forward 
Misconception/Error The student makes an error in using a trigonometric ratio to solve the problem. 
Examples of Student Work at this Level The student:
 Does not use the correct trigonometric ratio in the equation.
 Uses the tangent ratio but writes the equation incorrectly.

Questions Eliciting Thinking How did you choose which trig ratio to use?
What is the tangent ratio? What value should go in the numerator? What value should go in the denominator?
Can you explain how you tried to solve your equation? 
Instructional Implications Review the definitions of the trigonometric ratios. Then provide feedback to the student regarding any error made and allow the student to revise his or her work. Guide the student to carefully label given measures in diagrams and to consider if final answers make sense.
If needed, review how to solve equations of the form when the unknown is in the denominator. Provide additional opportunities to find an unknown length or angle measure in right triangles by using the Pythagorean Theorem or an appropriate trigonometric ratio.
Consider implementing other MFAS tasks for GSRT.3.8. 
Almost There 
Misconception/Error The student makes a minor computational or rounding error. 
Examples of Student Work at this Level The student labels the diagram correctly and writes correct equations involving the tangent ratio. However, the student:
 Does not round according to the directions of the problem.
 Calculates in radians instead of degrees when using a calculator.
 Makes an error using the table of trigonometric values.
 Makes a computational error when solving a correctly written equation.

Questions Eliciting Thinking According to the problem, how should you express your final answer?
What mode should your calculator be in?
There is a small error in your work. Can you find and correct it?
Can you show me how you used the trig table to find the angle measure? 
Instructional Implications Provide feedback to the student regarding any error made and allow the student to revise his or her work. Provide additional opportunities to find unknown lengths or angle measures in right triangles.
Introduce the student to the concept of solving a triangle (i.e., finding all angle measures and side lengths). Ask the student to solve right triangles given minimal information (e.g., the measure of an acute angle and one side or the measures of two sides).
Consider implementing other MFAS tasks for GSRT.3.8. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student draws a diagram for the problem and labels both the angles of depression from the lighthouse to each boat and the angles of elevation from each boat to the lighthouse.
The student then writes equations to find each distance:
After finding both distances the student subtracts to find the distance between the boats, 161 feet.

Questions Eliciting Thinking Can you think of another correct way to write the equation? How? 
Instructional Implications Challenge the student with more difficult, multistep problems that require the use of right triangle trigonometry and the Pythagorean Theorem. Consider introducing the student to the Law of Sines and the Law of Cosines and problems that can be solved using these laws.
Consider implementing other MFAS tasks for GSRT.3.8. 